Answer:
[tex]y=\dfrac{5}{6}x[/tex]
Step-by-step explanation:
A linear equation that shows a proportional relationship between two variables x and y can be expressed as:
[tex]y=kx[/tex]
where k is the constant of proportionality.
When x = 0, the equation becomes y = 0, which means that the line passes through the origin. So, a linear equation that shows a proportional relationship always passes through the origin.
Among the provided answer options, the only linear equation that is in the form y = kx, and therefore shows a proportional relationship, is:
[tex]\Large\boxed{\boxed{y=\dfrac{5}{6}x}}[/tex]
The remaining linear equations are in slope-intercept form, y = mx + b. This form implies that they intersect the y-axis at a point other than the origin, indicating they are not proportional relationships.
